Given $C = 130 ^ { \circ } , a = 16.9$, and $c = 12.3$, use the Law of Sines to solve the triangle (if possible) for the value of $b$. If two solutions exist, find both. Round answer to two decimal places.
A) $b = 3.73$
B) $b = 1.29$ and $5.61$
C) $b = 6.98$
D) $b = 0.36$ and $5.74$
E) not possible

Question

Quizplus · Accepted Answer

Given the angle $C = 130^\circ$ and sides $a = 16.9$ and $c = 12.3$, the Law of Sines can be applied. However, for a solution to exist, the side opposite the given angle must be the longest side in the triangle, because the sine function reaches its maximum value of 1. Since $a > c$ and $a$ is not opposite the given angle $C$, it violates this principle, making it impossible to solve the triangle with the given information.

Given C=130∘,a=16.9C = 130 ^ { \circ } , a = 16.9C=130∘,a=16.9

Given $C = 130 ^ { \circ } , a = 16.9$